Fermions

Fermions are a class of particles characterized by half-integer spin and the behavior that their quantum states obey Fermi-Dirac statistics. A defining consequence is the Pauli exclusion principle: no two identical fermions can occupy the same quantum state simultaneously. This antisymmetry of the many-body wavefunction under particle exchange leads to phenomena such as electron configuration in atoms and degeneracy pressure in dense stellar objects.

Fermions include two broad groups: elementary fermions and composite fermions. Elementary fermions are the quarks and leptons (six quark flavors: up, down, charm, strange, top, bottom; charged leptons: electron, muon, tau, and their neutrinos). Composite fermions include hadrons formed from quarks, notably baryons such as protons and neutrons, as well as many atomic nuclei with an odd number of nucleons. All fermions have half-integer spin, commonly 1/2, though higher half-integer spins also occur for some composite fermions (e.g., certain baryons can have spin 3/2).

Fermions and antiparticles: each fermion has a corresponding antiparticle with opposite quantum numbers. In many-body systems, fermions obey Fermi-Dirac statistics, giving rise to properties like the electronic structure of atoms, electron degeneracy pressure, and certain quantum phenomena such as superconductivity when fermions form pairs.

Relation to other statistics: bosons, which have integer spin, obey Bose-Einstein statistics and can occupy the same quantum state. The spin-statistics connection is a fundamental principle of quantum field theory.